# Difference between MT method and Hotering theory

The difference between the MT method and the hotering theory, but the simple difference is the difference between mahalanobis distance and T2 statistics.

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Difference between Mahalanobis distance and T2 statistics

Mahalanobis distances are also used with a scudded value (D2).

Thedifference between D2 and T2 is whether the co-variance used for calculation is mother co-variance or sample co-dispersion. D2 uses mothercovry variance, and T2 usessample covryn dispersion.

Note that some literature defines T2 as a further n-times the amount calculated by the above differences, but we do not know which is correct in the T2 definition expression.

In any case,however, the difference betweenD2 and T2 is the difference between mother and sample co-dispersions. Technically, it is the difference between using "n" or "n-1" in expressions that use co-distribution.

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There is no practical difference betweenMahalanobis distance and T2

Because of the above differences, there is no special difference between choosing Mahalanobis distance or T 2 whenusing it as an out-of-the-field indicator in the value model.

Some multi-varying chart usesD 2 and some use T2.

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Differences other than indicators

There is no significant difference between mahalanobis distance and T2, so the effects of the differences may not appear as described above, but when the theory is developed further, the direction is very different.

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Theory of using Mahalanobis distance

As I wrote on the Mahalanobis Distance page, mahalanobis distance is a natural extension of the euclidean distance that is commonly used on a daily basis, so it is easy to physically image.

The MT method using Mahalanobis distance has studied the theory of evaluating the selection of variables, y/ms.

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Theory using T2

T2 is part of the hotering theory. The hotering theory has been studied as a natural extension to the multi-randomity of the t-distribution.

Therefore, it can be used as a basic theory of multi-indestable statistics.

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